Does Math Lead to Understanding?

In "SolderSmoke -- The Book" I describe the quest for deep understanding of the circuits that we build and use. There is some discussion in the book of the role of mathematics in this quest. A while back a reader e-mailed me on this subject. In the hope of stimulating a discussion, I'll present the key paragraph from that e-mail here (the author will, for now, remain anonymous):

I appreciate your quotes from Feynman, Asimov, etc. about not
really being able to fully understand everything. As a math teacher
I can say that one of the biggest misunderstandings about math
is that it "explains" the phenomena of physics and engineering.
(Science and math teachers are notorious for saying to a student
who has just asked a "why" question things like, "well the math is
a little bit more complicated than what you can handle right now.
Wait untilyou have had a year or so of calculus.") In reality it's
the exact opposite! The math equations actually hide the answers.
They are very good at accurately describing phenomena, or at
predicting what will happen next, but they can never answer the
question of why one equation works and another does not. We
get very comfortable with allowing the familiar math equations
to hide our inability to really answer the "whys."

This really resonated with me. In my effort to get a better grasp of mixer theoy a lot of people seemed to be simply pointing me to the trig equations, and equating a knowledge of those equations with an understanding of how the mixer circuits really work.

Of course, I don't mean to be anti-math here, but I thought the e-mail on the limits of mathematics was very interesting. In "Empire of the Air" Tom Lewis wrote, "At Columbia, Edwin Howard Armstrong developed another trait that displeased some of the staff and would annoy others later in life: his distrust of mathematical explanations for phenomena of the physical world. All too often he found his professors taking refuge in such abstractions when faced with a difficult and seemingly intractable conundrum... Time and again as an undergraduate at Columbia, Armstrong had refused to seek in mathematics a refuge from physical realities."

My QSO with K4TWJ

Like everyone else I was saddened to hear of the passing of Dave Ingram. We've all been inspired by Dave's magazine articles, columns, and by his books. I'll always remember his QRP transmitter in a pen!
It was my privilege to talk to Dave once, on the air. I was on 30 meter CW with a brand new,scratch-built, HB QRP transceiver. I was in Virginia. I recognized Dave's call, and was thrilled when he came back to mine. I told him I was running homebrew QRP, and that I'd found inspiration in his articles. I know he was happy to hear that.
73 OM!
Dave's wife Sandy put a nice message on his blog: http://k4twj.blogspot.com

Some Real DX: Andromeda Galaxy, M31

I mentioned that Billy and I had spotted the Andromeda galaxy. The photo above (not by us) is sort of close to what we saw. The astronomy books usually show these spectacular images of Andromeda in all its glory. But those pictures come from long exposures through big telescopes. Through our little six inch reflector, Andromeda looks like a cloud, not quite as defined as the one in this picture. This picture is a 4 minute exposure through an ordinary digital camera using a 300mm telephoto lens.
(From: http://www.prairiehillfarmiowa.com/prairiehill/Home.html)

It is a real thrill to look at Andromeda. That little cloud represents 300 billion stars, and they are around 2.5 million light years away. So when you look, you know the photons hitting your retina started their trip LONG before there were homo sapiens. Icing on the cake: A satellite went through the telescope's field of view just as was looking at M31.

Another nice thing about Andromeda galaxy is that you can see it with the naked eye (you have to know where to look!). Because of this, people have been observing it for quite some time. Here is the first known drawing of M31. This is the work of the Persian astronomer Al-Sufi, and was done in year 964. The Persians imagined a constellation in the form of a fish in that part of the sky. Note the little cloud near the mouth of the fish -- that's M31.

Until 1923 astronomers thought M31 and other "nebula" were just clouds within our galaxy. The thought was that the Milky Way was the only galaxy. But then Edwin Hubble got some distance readings (using variable stars) on Andromeda and realized that he was looking at an entirely separate galaxy. That was a BIG discovery.

Homebrew transistors, QRSS Blog, Shep Show, Nose as toubleshooting tool

Some odds and ends today:

Ed, KC2TYP alerted me to this one: Jeff, K7JPD, has a very intriguing blog post about homebrew transistors. I suspect AA1TJ will have a rig made of these things on the air within a week. Check it out:
http://jeff-duntemann.livejournal.com/227856.html

There is a new blog for the Knights of the QRSS:
http://knightsqrss.blogspot.com/

Dave in Ireland sent me a link to the Jean Shepherd show in which he discusses his first soldering iron: http://www.archive.org/download/JeanShepherd1975/1975_07_30_Soldering_Iron_full_show.mp3

Alan, WA9IRS, alerted us to a nice EDN article on using your nose as a trouble-shooting tool:
http://www.edn.com/article/CA6713738.html

The Sabine Shack

How's that for a shack! Elisa rescued me from the frigid front porch and got the owner to agree to let me use this little building. You can see the VW solar panel in the window.

Here's the view:

Here's a little silent video we shot of the Sabine Shack:



The HW-8 runs of a 7AH Gell Cell that is charged by my Volkswagen panel. Antenna is a doublet fed by TV twin lead. The Blackberry provides internet access, and I can send in blog articles from it by e-mail.

Springtime on Mars (as seen from the Sabine hills)

Ian Sharp in Britain took this image at 0:54 UT January 4, 2010. The North Polar Cap is huge and obvious. The slightly bright region on the southern limb (top) is the dusty Hellas basin.

---

After months of looking at Jupiter, we now have a good view of Mars. On Saturday night we had a "Mars-rise" over Monte Calvo shortly after sunset. Mars is really bright now (explained below) and the distinctive red color really jumps out.

I didn't take the picture, but the shot above gives you a good idea of what I was looking at on Saturday night. The Northern polar cap was very apparent in my six inch Newtonian Dobsonian. It looked like it had a dark border around it. Martian North is at the bottom in this shot. It is Spring in the Northern hemisphere of Mars now.

Mars is now in a very good position for observation from Earth. On January 27, it will be in full opposition:

So hey, this is the time for those of you who are hoping to win the Elser-Mathes Trophy! Aim those Yagis and be sure to tune UP!

No smoke but Mars, Andromeda, and QRP

No podcast today because we are out in the Sabine hills.But here is a
report on activities here; RC plane was a flop. Advice from WA6ARA and
others helped, but wings are now really messed up. Big success in
astronomy: clear skies and no moon on Saturday. We had a really
beautiful "Mars rise" and were able to see the polar ice cap. Then we
spotted Andromeda galaxy naked eye, and then viewed it in the scope.
Awesome. I'm on the HW8 now. There is a contest but I've managed a few
real QSOs. Back to Rome tonight.

5X7JD: Tuna-Tin To... Uganda

SolderSmoke listeners might recall that Jack Dunigan e-mailed me prior to his move to Uganda. Jack had been listening to our stories about QRSS and WSPR and was thinking about setting up an East African beacon. Jack in now in Uganda and on the air as 5X7JD. He has a beautiful and very interesting blog. Check it out:

http://hamradiosafari.com/

(Jack: Maybe run WSPR using your computer and the Icom at low power, and then use the Tuna-Tin-Two for a separate QRSS beacon. You need an SSB rig for WSPR, but a simple K1EL keyer hooked up to the Tuna-Tin is all you would need for visual QRSS. The TT may need some modification to put it on 30 meters. Let us know if you need help, parts, crystals, etc. It would be a real hoot to have a Tuna Tin beacon from Uganda!)

Jack's blog is filled not only with tales of ham radio in Africa and Jack's personal radio roots (in his Dad's TV repair shop), but there is also information about the work that took Jack and his wife to Africa. Here is his description of it:

Aidchild, the organization for whom I work here in Uganda, cares for orphans living with Aids. There are two homes filled with kids for whom we care completely. This means we provide complete care because they are in every respect our own children. We also provide clinical and laboratory services for about 3000 more children. All of this costs money, lots of it. You can check us out at www.aidchild.org

We raise money through donations, but we also have started businesses here in Uganda to provide funds. We have an art gallery and shop at the Sheraton Hotel in Kampala, a gallery and cafe on the Equator, and a restaurant here in Masaka called Ten Tables (any guess as to how many tables there are?). But caring for Aids children is not inexpensive. So we can always use more funds.

From Jack's postings you also get a sense of the personal sacrifices and hardships that come with his kind of work: scroll down to his posting about malaria and you will see what I mean. As we all watch the suffering in Haiti, it is a good time to think about the many good people like Jack and his wife who are working hard to help our fellow human beings in difficult third-world areas.

Speaking of Haiti, of course the situation is unspeakably bad. We feel real connections to it: My wife is from the same island (from the Dominican Republic). When I was stationed in Santo Domingo, I traveled to Port-au-Prince, and went to many of the places that you now see (crumbled) on TV. Here in Rome, the principal at our kids' school is Haitian. And I have friends in our embassy there. As a kid, one of my first DX contacts was with HH2JT -- Jules Tomar (I still remember getting his QSL). I see that the good fellows at G-QRP have made a contribution to the relief efforts. We should all follow their lead. Graham, G3MFJ, reports that the club made their donation to :
http://www.dec.org.uk/donate_now/

VK6ADF: Echolink, WSPR, 6 Meter Yagi

From London I used to talk to Phil, VK6ADF, on Echolink. We have a lot of interests in common. This may be due to the fact that we were both born in the International Geophysical Year. Phil is now reading "SolderSmoke -- The Book," so we will probably discover other areas in which we have crossed paths. This week, I decided to get back onto Echolink, and in my first session I was looking for OM Phil. He wasn't on, but, IN A VERY MYSTERIOUS TWIST, that morning he sent me an e-mail. Spooky, eh? Anyway, yesterday we got on Echolink and covered our usual wide-range of tech topics. Phil alerted me to a web site called Real Flight that provides an on-line simulator for Radio Controlled airplane pilots. Obviously Billy and I could use some time in the simulator!
Phil is also into WSPR and as we spoke I fired up my 20 mW DSB WSPR rig. I was immediately heard by an Irish station, and Phil almost instantly saw the report on the WSPR database. I noticed that the EI station was reporting that I was on 40 meters, when in fact I was rock-bound on 30. Again, as Phil and I talked, I went to the WSPR chat section and asked about the freq discrepancy. Another VK6 (a friend of Phil's!) answered my question (a simple set-up problem). Small world.
Phil and I have similar curmudgeon-like thoughts on Surface Mount Soldering, and he seemed sympathetic when I said that I think I am more of a "Hardware Defined Radio" guy. Again, this may be an IGY thing. Oh yea, almost forgot: We're not crazy about LINUX either. We are only a few short steps away from the "SPARK FOREVER" mentality and full-fledged Luddite status.
One interest that Phil and I DO NOT share is Six Meters. Phil is now addicted to the Magic Band (which I still consider to be a white noise generator). Check out his video on his six meter yagi.

AA1TJ: Reggies Rule! Diode Amps! QRP to the Max!

Whenever I find myself in need of some radio-inspiration, an e-mail from Mike, AA1TJ, seems to pop up in my inbox. This morning's message and the associated video (above) were especially inspirational. Mike was e-mailing Steve, WA1HFF.

Hi Steve,
Thanks for the message and the great QSO! I was running my one transistor transceiver that I call the Reggie. You can read about it on my webpage at

http://mjrainey.googlepages.com/reggie

My antenna is nothing to write home about; just an end-fed half-wave wire bent into an "EL" at 35 feet.

I've made just over 240 contacts with my Reggie in a little more than a year's time; working 19 states. My best (and only) real DX was the Bahamas. All of these contacts were made with no receiver gain on this end; just a pair of diodes fed by a one-transistor BFO, and onto the headphones.

A couple of fellows have built their own Reggies, so you might run into one on 80m now and then. I've made three Reggie to Reggie QSOs thus far.

Steve, last night I was trying something new; I ran a loudspeaker from an audio amplifer connected to my Reggie. What's unusual is that my audio amplifer was made from three, common power supply rectifiers (1N5401's). I'm not kidding! It's a nearly forgotten circuit from 1954 that I (re)stumbled upon a couple of weeks ago. It uses the phenomenon of PN junction charge-storage to produce amplification.

Last week I used two diode gain stages for a total power gain of 48dB to drive my headphones. Yesterday, I added a third diode gain-stage and connected it to a loudspeaker for shack-filling audio volume.

I made a video of last night's setup (the same setup I worked you with). You can see it at

http://www.youtube.com/watch?v=3DA07A6BLDg

Thanks again for the nice contact last night, Steve. You were armchair copy here! :o)

Best wishes,
Mike, AA1TJ

Here's a question for Mike: Can you build that kind of amplifier with homebrew point-contact diodes? If so, you'd be opening up the possibility of a homebrew solid state receiver with homebrew solid state devices. Oh man, this stuff makes me feel like such an APPLIANCE OPERATOR.